3.1 Vector and Scalar Quantities What is a vector quantity? A vector quantity requires both magnitude and direction for complete description ex: acceleration, 6 m/s^2 (depends on direction) What is a scalar quantity? A scalar quantity is described by magnitude only and can be added, multiplied, subtracted, etc like normal numbers ex: mass and time, 50 grams or 10 seconds (does not depend on direction)
3.2 Velocity Vectors Arrows are used to represent the magnitude and direction of vector quantities. The length represents the magnitude, when drawn to scale and the direction of the arrow represents the direction of the vector. What are velocity vectors? A velocity is sometimes the result of combining multiple vectors. If groups of vectors are being added, their sum is called the resultant and can be found mathematically by using sine and cosine. To find the resultant using the pythagorean therom:
R^2= x^2 + y^2
ex: an airplanes velocity- combination of the planes velocity relative to the air and the velocity of the air relative to the ground.
3.3 Components of Vectors Any vector can be resolved into two component vectors at right angles to each other, these are called components. Resolution is the process of determining the components of a vector.
3.4 Projectile Motion Any object that moves through or above the air is known as a projectile.A projectiles horizontal motion is motion with a constant velocity and vertical motion of a projectile is a free fall.Vertical and horizontal motions of the projectile are independent of each other. ex: throwing a baseball- the horizontal motion causes it to travel farther with a changing velocity and the vertical motion is a constant free fall which causes it to inevitably hit the ground
3.5 Upwardly Launched Projectiles Anything that is launched upward at an angle will follow a curved path and return to earth, this is due to gravity.After 1 second, the object will be 5 m below the initial height, after 2 seconds it will be 20 m below it, etc.The horizontal component will not change at all, but the vertical change as the projectile moves.An object launched at 45°will travel farther than any other launch angle and one thrown straight up will reach max height. Equation for distance when an object is launched with an initial velocity of vi at an angle of θ (g being the gravitational acceleration constant):
d=vi^2sin(2θ) / g.
3.6 Fast Moving Projectiles – Satellites Something thrown or launch faster than around 8 km per second will never fall to the earth.The earth will curve away more quickly than the object can fall.This causes the object to go into orbit.This is known as a satellite.
3.1 Vector and Scalar Quantities
What is a vector quantity?
A vector quantity requires both magnitude and direction for complete description
ex: acceleration, 6 m/s^2 (depends on direction)
What is a scalar quantity?
A scalar quantity is described by magnitude only and can be added, multiplied, subtracted, etc like normal numbers
ex: mass and time, 50 grams or 10 seconds (does not depend on direction)
3.2 Velocity Vectors
Arrows are used to represent the magnitude and direction of vector quantities. The length represents the magnitude, when drawn to scale and the direction of the arrow represents the direction of the vector.
What are velocity vectors?
A velocity is sometimes the result of combining multiple vectors. If groups of vectors are being added, their sum is called the resultant and can be found mathematically by using sine and cosine. To find the resultant using the pythagorean therom:
R^2= x^2 + y^2
ex: an airplanes velocity- combination of the planes velocity relative to the air and the velocity of the air relative to the ground.
3.3 Components of Vectors
Any vector can be resolved into two component vectors at right angles to each other, these are called components. Resolution is the process of determining the components of a vector.
3.4 Projectile Motion
Any object that moves through or above the air is known as a projectile. A projectiles horizontal motion is motion with a constant velocity and vertical motion of a projectile is a free fall. Vertical and horizontal motions of the projectile are independent of each other.
ex: throwing a baseball- the horizontal motion causes it to travel farther with a changing velocity and the vertical motion is a constant free fall which causes it to inevitably hit the ground
3.5 Upwardly Launched Projectiles
Anything that is launched upward at an angle will follow a curved path and return to earth, this is due to gravity. After 1 second, the object will be 5 m below the initial height, after 2 seconds it will be 20 m below it, etc. The horizontal component will not change at all, but the vertical change as the projectile moves. An object launched at 45° will travel farther than any other launch angle and one thrown straight up will reach max height.
Equation for distance when an object is launched with an initial velocity of vi at an angle of θ (g being the gravitational acceleration constant):
d=vi^2sin(2θ) / g.
3.6 Fast Moving Projectiles – Satellites
Something thrown or launch faster than around 8 km per second will never fall to the earth. The earth will curve away more quickly than the object can fall. This causes the object to go into orbit. This is known as a satellite.